Gotta love Stackpole books for reprinting some of the manuals from the war. This sheds even more light than what we have already discussed on the Veteran Volunteers. From The 1865 Customs of Service for Non-commioned Officers and Soldiers by August V Kautz, pages 197-198:

VETARANS

590. VOLUNTEERS who have served at least nine months, and who re-enlist, are entitled to be called "Veteran Volunteers," and may wear the service chevron showing they served one enlistment. (G.O. No. 191, 1863.)

591. Veterans are entitled to one month's advance pay, a premium of two dollars, and bounty amounting in all to four hundred and two dollars, to be paid by installments as provided by G.O. No. 191, Par 30. If discharged before the expiration of their enlistment, veterans will recieve the balance on the foregoing bounty. The heirs of veterans who die in service will be entitled to the balance of the above bounty remaining unpaid at the time of death.

592. Soldiers who re-enlisted prior to June 25, 1863, and who have complied with the conditions promulgated in G.O. No. 191 of that date, are entitled to the bounty therein provided; that is, they must have served one enlistment of at least nine months, and been regulary and properly mustered into service. (G.O. No. 216, 1863.)

593. A veteran regiment, to entitle it to be called such, must be composed of at least one-half it's number of men who have served one enlistment of not less than nine months. (G.O. No. 216, 1863.)

Thinking about kj3553's post inspired me to look through The 1863 Laws of War manual (another Stackpole Books reprint to see what it said there. And either the War Department left it out of the original or Stackpole Books left it out of the reprint. You go through that book there are places where whole paragraphs are missing. And of course it might not have ever been in there, though part IV is "Extracts from the Revised United States Army Regulations of 1861 with an Appendix containing the Changes and Laws Affectinf Army Regulations to June 25, 1863." that's one reason why I thought it might have been there. But it does say to June 25th and the appendix does say up to June 25th, not from June 25th, so I'm probably wrong.